Intuitionistic uniformity principles for propositions and some applications

This note deals with the prepositional uniformity principlep-UP: p x N A (p, x) x N p A (p, x) ( species of all propositions) in intuitionistic mathematics.p-UP is implied by WC and KS. But there are interestingp-UP-cases which require weak KS resp. WC only. UP for number species follows fromp-UP by extended bar-induction (ranging over propositions) and suitable weak continuity. As corollaries we have the disjunction property and the existential definability w.r.t. concrete objects. Other consequences are: there is no non-trivial countable partition of;id is the only injective function from to; there are no many-place injective prepositional functions; card () is incomparable with the cardinality of all metric spaces containing at least three elements.     

Methadone maintenance: The addict's family recreated

A study of four methadone clinics, the addicts treated at these clinics, and their families, reveals basic dissonances in treatment ideology and professional-paraprofessional relationships which, combined with the addict's particular mode of functioning, make significant change in his behavior improbable. Addiction, as used here, is a class of behaviors in which the addict acts purposefully to acquire heroin but concurrently defines this behavior as the result of an out-of-control craving. This is an adaptive response to contingencies in his natal family.Both the natal family of the addict and the methadone clinics will be described as aspects of a social system characterized by the paradoxical injunction be out-of-control, communicated to the addict by those in the system and his response. Dissonandes in the functioning of both the addict's family and the methadone clinics are transformed into the flaw in the addict that results in the behavior defined as his addiction.This transformation is maintained by the treatment provided by the clinics, described as a ritual whose covert function is the maintenance of dissonances in the system within tolerable limits, through fomalized procedures. This implicitly validates both the formal structure of the clinic and the flaw in the addict. At the same time, addictive behavior creates and maintains an increasingly inclusive social system characterized by similar core dissonances.     

Независимость одной системы аксиом и правила вывода пропозиционального исчисления

- Allatum est die 5 Martii 1970     

Inverses for Normal Modal Operators

Given a 1-ary sentence operator , we describe L - another 1-ary operator - as as a left inverse of in a given logic if in that logic every formula is provably equivalent to L. Similarly R is a right inverse of if is always provably equivalent to R. We investigate the behaviour of left and right inverses for taken as the operator of various normal modal logics, paying particular attention to the conditions under which these logics are conservatively extended by the addition of such inverses, as well as to the question of when, in such extensions, the inverses behave as normal modal operators in their own right.     

Treating connectionism properly: Reflections on Smolensky

Summary In this essay, I undertake to examine the principal theses of Paul Smolensky's 1988Behavioral and Brain Sciences target article, On the proper treatment of connectionism, from the point of view of the methodology and epistemology of science, that is, the philosophical theory of theories in general. After exploring the instrumentalist and realist views of the relationships between micro- and macrotheories on their home ground in the natural sciences, the procedures by which a phenomenally described cognitive task is prepared for symbolic or subsymbolic modeling, and the contrast between the deliberate conscious reasoning processes of a novice and intuitive behavior of an expert in solving a given family of cognitive problems, I argue that although Smolensky is right about what it would take for connectionist subsymbolic models to relate to symbolic models as micro- to macrotheories, he is wrong in concluding that they do. On the contrary, it would be something of a miracle if the idealized nomological structure of the behavior of stochastic patterns of activity over large numbers of subsymbolic units in a connectionist machine corresponded even approximately to the nomological structure of the conceptual level behavior of a Von Neumann computer running off a program whose syntax had been explicitly designed to structurally operationalize a determinate fragment of intentional semantics — unless, of course, the connectionist machine had been deliberately constructed to implement the symbol processor in the first place.I conclude that the proper treatment of connectionism is to be found among the blandly ecumenical proposals for irenic cooperation and division of labor that Smolensky considers and rejects.     

Personality dimensions and domains of service performance: A field investigation

Although recent meta-analytic studies have investigated the validity of the Big Five domains of personality by classifying pre-existing personality measures into the five dimensions, published validity studies incorporating explicit measures of the five broad traits are rare. This concurrent validity study examines relationships between direct measures of Big Five traits and job performance for a sample of 105 service workers. Analyses specifically examine relationships between three personality dimensions and factorally independent domains of service performance. Both conscientiousness and extraversion are found to correlate with specific performance dimensions. Contrary to our expectation, the extraversion-performance relationship is, however, negative.     

Sex differences in susceptibility to social influence

Sex differences in compliance and persuasiveness were examined while varying the sex-role relevance of the stimulus. Undergraduate students were asked to respond to opinion statements previously discussed by a fictitious group. Subjects read the group's unanimous opinion accompanying each statement and were told they would participate in a discussion with this group. Some subjects responded to statements about female sex-role relevant activities and others to statements about male sex-role relevant activities. Sex of influence source was manipulated by showing subjects all male or all female names of group members. Compliance was measured by the extent to which a subject's response approximated the group's opinion. The results show that males were more compliant than females when the stimulus statements concerned female sex-role-related activities and that females were more easily influenced when they responded to statements about male sex-role-related activities. Further, subjects were somewhat more easily persuaded by women on female sex-role-related activities and more influenced by men's opinions on issues relevant for males.In most of the social influence literature, alterations in a subject's behavior in an experimental situation has been termed conformity. However, conformity may involve either private acceptance or overt alterations in behavior without cognitive change (i.e., compliance). Throughout this article the term compliance refers to shifts in behavior toward an immediate and transitory social influence (Sherif & Sherif, 1969, p. 191).     

The Deep Structure of Group Life: Unconscious Dimensions

There is a reconsideration and renaissance of interest in expanded conceptions of unconscious processes as they affect individuals and groups (Grotstein, 1999). Recent focus on social unconscious (Hopper, 1996) and cultural unconscious processes (Henderson, 1988) and the nature of intersubjectivity (Harwood and Pines, 1998) raise questions about the location of group analysis. This paper considers the deep structure of group life by examining four functions of the unconscious: repressive, conservative, creative, and mythopoetic (Ellenberger, 1970). On an individual level of analysis, these functions are equated respectively with formative ideas about the: personal–subjective, social–political, intersubjective–cultural and collective–objective unconscious. Group level analogs, as they develop and affect groups and their members, are explored as synthetic, shared, symbolicy and synchronous unconscious processes.     

On a problem of P(α, δ, π) concerning generalized Alexandroff s cube

Universality of generalized Alexandroff's cube plays essential role in theory of absolute retracts for the category of , -closure spaces. Alexandroff's cube. is an , -closure space generated by the family of all complete filters. in a lattice of all subsets of a set of power .Condition P(, , ) says that is a closure space of all , -filters in the lattice ( ), .Assuming that P (, , ) holds, in the paper [2], there are given sufficient conditions saying when an , -closure space is an absolute retract for the category of , -closure spaces (see Theorems 2.1 and 3.4 in [2]).It seems that, under assumption that P (, , ) holds, it will be possible to givean uniform characterization of absolute retracts for the category of , -closure-spaces.Except Lemma 3.1 from [1], there is no information when the condition P (, , ) holds or when it does not hold.The main result of this paper says, that there are examples of cardinal numbers, , , such that P (, , ) is not satisfied.Namely it is proved, using elementary properties of Lebesgue measure on the real line, that the condition P (, ₁, 2 ) is not satisfied.Moreover it is shown that fulfillment of the condition is essential assumption in, Theorems 2.1 and 3.4 from [1] i.e. it cannot be eliminated.     

A note on the ω-incompleteness formalization

The paper studies two formal schemes related to -completeness.LetS be a suitable formal theory containing primitive recursive arithmetic and letT be a formal extension ofS. Denoted by (a), (b) and (c), respectively, are the following three propositions (where (x) is a formula with the only free variable x): (a) (for anyn) ( _T (n)), (b) _{T x} Pr _T (^–(x)^–) and (c) _T x(x) (the notational conventions are those of Smoryski [3]). The aim of this paper is to examine the meaning of the schemes which result from the formalizations, over the base theoryS, of the implications (b) (c) and (a) (b), where ranges over all formulae. The analysis yields two results overS : 1. the schema corresponding to (b) (c) is equivalent to ¬Cons _T and 2. the schema corresponding to (a) (b) is not consistent with 1-CON _T. The former result follows from a simple adaptation of the -incompleteness proof; the second is new and is based on a particular application of the diagonalization lemma.Presented byMelvin Fitting     

“God as Friend”: Metaphoric Theology in Pastoral Care

Because of postmodernity's claim of deconstruction, the naming of God has become a crucial issue for a hermeneutics of pastoral care. Inadequate and inappropriate perceptions of God, because of specific experiences of faith, create unhelpful images of God which eventually lead to a pathology of faith. Taking into consideration the figurative means of symbolic language and its rootedness in culture, this article explores the possibility of the metaphor, God as Friend, in order to move beyond the paradigm of the suffering God (theopaschitic theology) to the paradigm of the faithful God—God as our Soul Friend.     

Does Alternating Between Masculine and Feminine Pronouns Eliminate Perceived Gender Bias in Text?

This study explores whether alternating betweenthe pronouns he and she ina text is an effective way to avoid sexist language.Participants were psychology students at a largemidwestern university and were predominately White and frommiddle-class backgrounds. Students read two versions ofan essay, one that alternated between masculine andfeminine pronouns and one that exclusively used paired, he or she-type pronouns. Readersperceived the alternating version to be biased in favorof females and lower in overall quality than the pairedversion. However, the alternating version appeared to be more effective at combating sexism,suggesting an alternating strategy may be desirable forauthors with this goal. If the author is not primarilyconcerned with increasing readers' awareness of gender issues, techniques such as pluralization or thesingular they may be moreappropriate.     

O pojęciu zdania analitycznego

Rezultaty przedstawione w pracy niniejszej pokrywaj si czciowo z wynikami osignitymi przezR. Wójcickiego w pracy:Analityczne komponenty definicji arbitralnych. Studia Logica, t. XIV. Dotyczy to gównie rezultatów zawartych w czci pierwszej. Chciabym podkreli, i wyniki R. Wójcickiego uzyskane zostay cakowicie niezalenie od rezultatów przedstawionych w pracy obecnej.Allatum est die 16 Aprilis 1962     

Managerial Stress, Locus of Control, and Job Strain in Taiwan and UK: A Comparative Study

This study investigated managerial stress in Taiwan and UK using the Occupational Stress Indicator-2 (OSI-2) and the Work Locus of Control (WLCS) scale. Results showed that the reliability and validity of the measures used were acceptable and comparable in the two samples. There were similarities as well as differences in managerial stress in the two countries. Recognition and Managerial role were important predictors of strain for the Chinese managers, whereas Relationships, Organizational climate, and Personal responsibility were important predictors of strain for UK managers. There were consistent moderating (vulnerability) effects of internal control for the Taiwanese managers. Results corroborated some previous studies conducted in the West. However, caution was also suggested for generalizing Western-originated concepts and theories across cultural boundaries.     

Some modifications of Scott's theorem on injective spaces

D. Scott in his paper [5] on the mathematical models for the Church-Curry -calculus proved the following theorem.A topological space X. is an absolute extensor for the category of all topological spaces iff a contraction of X. is a topological space of Scott's open sets in a continuous lattice.In this paper we prove a generalization of this theorem for the category of , -closure spaces. The main theorem says that, for some cardinal numbers , , absolute extensors for the category of , -closure spaces are exactly , -closure spaces of , -filters in , >-semidistributive lattices (Theorem 3.5).If = and = we obtain Scott's Theorem (Corollary 2.1). If = 0 and = we obtain a characterization of closure spaces of filters in a complete Heyting lattice (Corollary 3.4). If = 0 and = we obtain a characterization of closure space of all principial filters in a completely distributive complete lattice (Corollary 3.3).     

⊃E is Admissible in “true” relevant arithmetic

The system R## of true relevant arithmetic is got by adding the -rule Infer xAx from A0, A1, A2, .... to the system R# of relevant Peano arithmetic. The rule E (or gamma) is admissible for R##. This contrasts with the counterexample to E for R# (Friedman & Meyer, Whither Relevant Arithmetic). There is a Way Up part of the proof, which selects an arbitrary non-theorem C of R## and which builds by generalizing Henkin and Belnap arguments a prime theory T which still lacks C. (The key to the Way Up is a Witness Protection Program, using the -rule.) But T may be TOO BIG, whence there is a Way Down argument that produces a better theory TR, such that R## TR T. (The key to the Way Down is a Metavaluation, on which membership in T is combined with ordinary truth-functional conditions to determine TR.) The result is a theory that is Just Right, whence it never happens that A C and A are theorems of R## but C is a non-theorem.     

The treatment of adolescents and their families in cultural transition: Issues and recommendations

Increasing numbers of immigrant families with adolescent children are seeking therapy because of intergenerational conflicts specific to the adolescent separation-individuation phase of the life cycle and transitional problems related to immigration and cultural transition. Three types of adolescent immigrants are identified and discussed: Immigrants (subtypes Reluctants and Optimists), Immigrant-Americans, and Americans. Therapists' issues which can negatively affect therapy with such adolescents and families are also discussed. Effective therapy with immigrant families requires that family therapists become more culturally sensitive, therapeutically flexible, and accepting of family values to which they may be diametrically opposed. Recommendations for therapy are offered.Dr. Baptiste is himself an immigrant. The experiences and observations discussed here are culled from his work with immigrant families and children over the past 19 years in the District of Columbia, Massachusetts, Indiana, and New Mexico.Portions of this article will appear in a chapter Psychotherapy with adolescent immigrants and their families in cultural transition in B. Settles and D. Hanks (Eds.),Families on the move: Emigration, immigration, migration and mobility. Sage Publications, 1990, and are used here with permission.     

Toward a model for spirituality and alcoholism

Spirituality is a significant factor in recovery from alcoholism, whatever definition of this condition one may use. One aspect of alcohol abuse is its apparent relationship to the balance between brain hemispheres. Excessive use of alcohol anesthetizes the object-based, language-oriented functions of the left hemisphere, associated with an action mode of consciousness. This allows greater engagement of the right-hemisphere receptive mode, which is also associated with religious experience. A model of spirituality based on achieving a balance between hemisphere functions and modes of consciousness could provide a non-chemical alternative to excessive use of alcohol.     

The ω-rule

We prove that all proofs in -logic (a first order logic with -rule added) in which -rule is used finitely many times can be turned into proofs in which the -rule is used at most one time. Next, we prove that the word finitely above cannot be changed by the word infinitely.     

On Some Kripke Complete and Kripke Incomplete Intermediate Predicate Logics

The Kripke-completeness and incompleteness of some intermediate predicate logics is established. In particular, we obtain a Kripke-incomplete logic (H* +A+D+K) where H* is the intuitionistic predicate calculus, A is a disjunction-free propositional formula, D = x(P(x) V Q) xP(x) V Q, K = ¬¬x(P(x) V ¬P(x)) (the negative answer to a question of T. Shimura).